In a series of rulings on Wednesday, Judge Elyakim Rubenstein rejected the appeals by four families.
But in a fifth case, it asked the state to justify its planned demolition over an attack in which the victim was wounded but not killed.
According to court documents seen by AFP on Thursday, the first case was filed by the family of Mohammed Jaabis, 23, from Jabal Mukaber, who rammed an earthmover into a bus on August 4, killing an Israeli and wounding four others. He was shot dead by police at the scene.
The judge also rejected an appeal by the family of Ibrahim Akari, 38, from Shuafat refugee camp, who on November 5 rammed his car into pedestrians, killing a teenager and a policeman and wounding nine, before also being shot dead.
Also rejected was an appeal by the families of Uday and Ghassan Abu Jamal, cousins from Jabal Mukaber who on November 18 attacked a Jerusalem synagogue with meat cleavers and a gun, killing four rabbis at prayer and a policeman.
But Rubenstein did not reject the appeal by the family of Muataz Hijazi, 32, from Abu Tor, who on October 29 tried to gun down a right-wing Jewish activist, critically wounding him. Hijazi was shot dead the next morning during a police raid.
Instead, the judge ordered the state to explain why it would not halt the demolition order given that the victim did not die.
"Even though the acts attributed to Muataz were very serious indeed, they did not ultimately result in the loss of human life," Rubenstein wrote.
"The state must examine very carefully every possible alternative to demolishing the house," he said, requesting a response within 15 days.
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The court also rejected a broader appeal by eight human rights groups against the policy of demolishing the homes of Palestinian attackers, which has been slammed as collective punishment targeting not the perpetrators but their families.
"I cannot deny this appeal raises difficult questions ... and an ethical dilemma," Rubenstein wrote.
"But the chance that destroying a home or sealing it could prevent future bloodshed obliges us to harden our hearts and spare lives .. than to spare the occupants of a house."
Israel used punitive house demolitions for years in the West Bank but the policy was halted in 2005 after the army said they had no proven deterrent effect and was likely to encourage violence.
But on November 6, following two deadly car attacks in a fortnight, Israel's decided to resume the policy.
Two weeks later, Israeli forces demolished the home of the family of Abdelrahman Shaludi, a Palestinian who deliberately rammed his car into a crowd of pedestrians on October 22, killing a young woman and a baby.
The attacks took place as a wave of violent unrest swept Jerusalem that began as Israel pressed a major 50-day offensive against militants in Gaza but which tailed off towards the end of the year.